Open AccessType 2 degenerate modified poly-Bernoulli polynomials arising from the degenerate poly-exponential functions
Author(s) -
Dojin Kim,
Patcharee Wongsason,
Jongkyum Kwon
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022541
Subject(s) - degenerate energy levels , bernoulli polynomials , bernoulli number , mathematics , logarithm , exponential function , stirling number , pure mathematics , stirling numbers of the second kind , type (biology) , euler's formula , difference polynomials , combinatorics , orthogonal polynomials , mathematical analysis , physics , quantum mechanics , ecology , biology
We present a new type of degenerate poly-Bernoulli polynomials and numbers by modifying the polyexponential function in terms of the degenerate exponential functions and degenerate logarithm functions. Also, we introduce a new variation of the degenerate unipoly-Bernoulli polynomials by the similar modification. Based on these polynomials, we investigate some properties, new identities, and their relations to the known special functions and numbers such as the degenerate type 2-Bernoulli polynomials, the type 2 degenerate Euler polynomials, the degenerate Bernoulli polynomials and numbers, the degenerate Stirling numbers of the first kind, and $ \lambda $-falling factorial sequence. In addition, we compute some of the proposed polynomials and present their zeros and behaviors for different variables in specific cases.